Let a → , b → and c → be three non - zero vectors such that no two of them are collinear and a → × b → × c → = 1 3 b → c → a → . If θ is the angle between vectors b → and c → , then a value of sin θ i

Question

Let a → , b → and c → be three non - zero vectors such that no two of them are collinear and a → × b → × c → = 1 3 b → c → a → . If θ is the angle between vectors b → and c → , then a value of sin θ is

TestHub · Accepted Answer

Given a → × b → × c → = 1 3 b → c → a → a → ⋅ c → b → - b → ⋅ c → a → = 1 3 b → c → a → ⇒ a → ⋅ c → = 0 and b → ⋅ c → = - 1 3 b → c → b → c → cos θ = - 1 3 b → c → cos θ = - 1 3 sin θ = 1 - 1 9 = 8 9 = 2 2 3

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